Abstract: . . .  s r B (x 2 - V B ) + ux 1 C s ?x 3 = (ax 3 +ß)(x 3 -x 1 ) c e (k 1 a-k 2 ax 3 -k 2 ß) (7) III. Nonlinear control law The control of this system consists in changing the PWM ratio to obtain wether a desired output voltage, nor a de- sired output current nor a desired output power depending on control objective. A. Objective of the control We consider is this paper that the main objective is to charge the battery. An usual way [5] to do that is to max- imize the power absorbed by the battery. B. Nonlinear control of the whole system B.1 Flat control of the DC-DC control Sira Ramirez in [1] has proposed to use the output flat z = L 2 x 2 1 + C 2 x 2 2 to perform a flat control [6] of the DC-DC converter(1). A such control is very interesting because it takes into account the internal dynamic of the system. However, this control cannot be directly applied if the ex- ternal voltage E is uncertain [7]. In our case, E is issue from the solar panel, and isn’t obviously a constant value. Moreover . . .
. . .  4115–4120. [4] Boitier V., “???,” Rapport Laas numero ??, 2002. [5] Z. Eux, “Biduli’ck,” ? Pif gadget ??, 2000. [6] M. Fliess, J. Levine, P. Martin, and P. Rouchon, “Flatness and defect of non linear systems. introductory theory and examples,” Int. Journal of Control, vol. 61, pp. 1327–1361, 1995. [7] V. Mahout, “On the robustness of a flat control,” in to appear in ISC3, juin 2003. [8] A. Isidori, Non linear control systems, Springer, New York, 1995. [9] H. Nijmeijer and A. J. Van der Schaft, Dynamical control systems, Springer, New York, 1995.  . . .
. . .  are presented and differ- ent tests, like the reaching of the maximum of power, are discussed. Keywords—Nonlinear control, photovoltaic converter, DC- DC converter I. Introduction Non linear control laws are used in order to increase dy- namical performance of a system [8]. Indeed, as these tech- niques can take into account internal dynamics of a system (it is the case in particular for flat control), generally a more effective control can be expected. The system considered in this paper is a photovoltaic (PV) array which must pro- vide the electrical energy to recharge a battery. Between the panel and the battery exists a controllable system, a DC-DC converter, which ensures the regulation of the ten- sion and/or electric power at the terminal of the battery voltage. A non linear control is developed for this system. In a first part the problem of modelisation is presented. This system being constituted by three subsystems, the different models will be exposed before deducing the non . . .
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